Simplify the following expression: $ t = \dfrac{-2k + 8}{-k + 1} + \dfrac{-9}{2} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-2k + 8}{-k + 1} \times \dfrac{2}{2} = \dfrac{-4k + 16}{-2k + 2} $ Multiply the second expression by $\dfrac{-k + 1}{-k + 1}$ $ \dfrac{-9}{2} \times \dfrac{-k + 1}{-k + 1} = \dfrac{9k - 9}{-2k + 2} $ Therefore $ t = \dfrac{-4k + 16}{-2k + 2} + \dfrac{9k - 9}{-2k + 2} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-4k + 16 + 9k - 9}{-2k + 2} $ $t = \dfrac{5k + 7}{-2k + 2}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-5k - 7}{2k - 2}$